Role of interface tension in the thermoelastic analysis of inclusions: Unified formulation and closed-form results

Abstract

AbstractWe study the thermoelastic problem of an inclusion of general shape surrounded by a foreign elastic matrix under plane deformation and the influence of an in-plane far-field heat flux. The small-scale interface effects, related to not only interface conductivity, interface stretching rigidity and interface thermal expansion but also (residual) interface tension, are incorporated in the corresponding analysis. We establish general boundary value formulations in both heat conduction and thermoelasticity for an arbitrary inclusion shape, allowing for analytic or at least semi-analytic treatment of the problem. Specially, we derive closed-form solutions for the case of circular inclusion and obtain concise expressions for describing the remote heat flux-induced thermal stress near the interface (at both the inclusion side and matrix side). Surprisingly, it is shown that for the case of circular inclusion, interface tension plays the same role as interface stretching rigidity in determining the full thermal stress field, or in other words, the full thermal stress field depends on only the sum of interface tension and interface stretching rigidity but not on the specific value of either of them. Numerical examples are also given to illustrate the influence of interface tension on the von Mises stress distribution in the vicinity of the interface.Keywords: Conductive interfaceheat fluxinterface elasticityinterface tensionthermal stress Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingDai appreciates the support of the National Natural Science Foundation of China (No. 11902147), the Natural Science Foundation of Jiangsu Province (No. BK20190393) and the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) (Grant No. MCMS-I-0222Y01).